Device for concentrating or collimating radiant energy

ABSTRACT

This invention consists in a nonimaging device for concentration or collimation of radiation on a receiver or from an emitter ( 14 ), depending on the case. The device is made up of the lens ( 50 ), which surrounds the receiver and consists of the aspheric surface ( 21 ), and the lens ( 15 ), whose upper refractive surface ( 16 ) may be aspheric, while the lower surface is aspheric ( 17 ) in its central portion (between points  18  and  19 ) and has a structure with discontinuous slope ( 20 ) in its external portion, in which the faces ( 22 ) fundamentally refract the rays while the faces ( 23 ) reflect them by total internal reflection. The design method provides that the device properties of concentration/collimation are noticeably superior to those of the existing inventions.  
     Possible applications of this lens include: radiation sensors, illumination systems with LEDs, wireless optical communications and photovoltaic solar energy.

TECHNICAL SECTOR

[0001] It falls within the category of optical systems; specifically,that of Nonimaging Optics.

PREVIOUS TECHNIQUES

[0002] There exist previous inventions related to the present invention,all related to one another, for which various patents have been takenout (U.S. Pat. Nos. 4,337,759; 5,404,869; 5,577,493). While in a generalway some of the possible geometries of the present invention arequalitatively similar to those of these previous inventions, there areseveral fundamental differences that make this invention novel, and ruleout any conflict with the others. These differences lead to the opticalsurfaces of the invention being substantially different, due to the factthat the conditions imposed on their design are different, and thereforealso their resulting optical performance. In particular, the inventionpresented here can work very close (>95%) to the thermodynamic limit ofconcentration/collimation, while the previous inventions, not based onthe tools of Nonimaging Optics, are well short of this limit (<80%) whenthe angular spread of the ray bundles on passing through any of theoptical surfaces is large (>10°).

[0003] The related patents are: the patent of Popovich et al. U.S. Pat.No. 4,337,759,July/1982; that of W. A. Parkyn, Jr. et al., U.S. Pat. No.5,404,869, April/1995, and lastly, that of W. A. Parkyn, Jr. et al.,U.S. Pat. No. 5,577,493, November /1996.

[0004] The designs of all the mentioned inventions are not based (incontrast to this one) on the edge-ray theorem of Nonimaging Optics, sothat their functioning is limited with the extended bundles produced bymany emitters and receivers used in practice. The patents U.S. Pat. No.4,337,759,July/1982 and U.S. Pat. No. 5,404,869, April/1995 consideronly the central ray of the bundles in the design. U.S. Pat. No.5,577,493, November/1996 considers the so-called first-order opticsaround the central ray (Luneburg, 1964), which provides an order ofapproximation superior to the previously-mentioned device, but even so,the performance attributed to it by its inventors for producing constantirradiance is only accurate for bundles with very small angular spread.

[0005] Furthermore, the invention protected by U.S. Pat. No. 5,577,493,November/1996 is axisymmetrical and considers as output bundle thatproduces uniform irradiance in 3D at the exit aperture. This bundle isonly a particular case of those considered in the present patent.

DESCRIPTION OF THE INVENTION

[0006] This invention consists in a nonimaging concentration orcollimation device made of two aspheric lenses, one of them containing astructure with discontinuous slope (i.e., faceted), that concentrate theradiation incident on a receiver or collimate the radiation from anemitter, depending on the case. The design method of this concentratoris based on the nonimaging design method of Simultaneous MultipleSurfaces or SMS (Miñano, González, 1992).

[0007] For the design of this invention two extended (e.g., notpunctual) ray bundles are coupled in two-dimensional geometry (2D). Theactual three-dimensional (3D) devices are obtained by rotationalsymmetry (axisymmetrical) or translational symmetry (cylindrical), andtheir operation is analyzed a posteriori. Common examples of ray bundles(FIG. 1) are: (type 1) that composed of rays impinging on a segment (1)forming an angle inferior to a given angle (2) (called the acceptanceangle of the bundle) with the perpendicular to this segment, and (type2) that composed of the rays that intercept two given segments (3). Bothtypes of bundle can be defined in a more general way (type 3) if thesegments are substituted by arbitrary curves. FIG. 1 shows, in additionto two bundles of types 1 and 2, a bundle of type 3 composed of the raysthat intercept a rectangle (4) and a semicircumference (5) (this bundleis useful for modeling an LED or an IRED). Another bundle of rays (type4) can be described, with a more general character than those of types 1and 2 (which includes them as particular cases), as that composed of therays that impinge on a segment with an angle of incidence between twospecified angles for each point of the segment.

[0008] The design of the present invention is based on the so-callededge-ray theorem of Nonimaging Optics (Welford, Winston, 1989), whichstates that to couple two bundles associated with the emitter and thereceiver it is necessary and sufficient to couple the subsets of edgerays of the two. The use of this theorem is the key to obtaining devicesthat work very close to the thermodynamic limit with bundles with wideangular spread. For example, the edge rays of the bundles in FIG. 1 are,for the type 1 bundle, those that impinge on the segment with an angleof incidence equal to the acceptance angle of the bundle and those thatpass through the edges (6) and (7) of the segment; for the type 2bundle, those that pass through any of the edges (8), (9), (10) and (11)of the two given segments; and for the type 3 bundle, those that aretangent to the rectangle and those that pass through edges (12) and (13)of the semicircumference.

[0009] A possible configuration of the invented device is that shown inFIG. 2, which also shows its basic working principle as a concentratorof radiation on a receiver (14). The lens (15) L₁ has two active faces:the upper refractive surface (16), referred to as S₁, which is ingeneral aspheric, and the lower one, S₂, which consists of anotherrefractive aspheric surface (17) in its central portion (between points(18) and (19), which we shall call P and P′, respectively) and astructure with discontinuous slope (20) in its external portion. Thelens (50) L₂ surrounds the receiver and consists of the refractiveaspheric surface (21), which we shall call S₃. The collected rays thatimpinge on the central portion (17) undergo three consecutiverefractions before reaching the receiver. On the other hand, thecollected rays that impinge on the more external portion (20) undergothe following incidences before reaching the receiver: a firstrefraction on the surface S₁, a (possible) total internal reflection onthe face (22) (which we shall call face V) of the teeth of S₂, a totalinternal reflection on the face (23) of those teeth (which we shall callface T), a second refraction on face V, and finally, a third refractionon S₃. The total internal reflection occurs when the angle of incidenceof the ray with the normal to the surface is greater than the so-calledcritical angle of the interface, which is given by sin⁻¹(1/n), n beingthe refractive index of the lens L₁.

[0010] Particular cases are those in which the profile of S₁ is circularor flat. The latter case is of especial interest in certainapplications, such as photovoltaic concentration, since it permits thegrouping of a set of devices fixed to a dielectric plate, such as a flatpiece of glass, which acts as a reference to provide parallelism betweenthe devices, as protection against the elements and as a filter forultraviolet radiation.

[0011] In the design the surfaces S₂ and S₃ are calculated from thespecification of the profile of the surface S₁ and of the input andoutput bundles. The definition of the input bundle can be made beforeits refraction on S₁, so that its definition would be independent ofthat of that surface. For example, it could be a type 1 bundle withacceptance α and with the edges of the segment coincident with theextreme points of the surface S₁. Another possibility, which could beinteresting in practice, is that of defining the input bundle after itsrefraction on S₁, which allows, for example, the segment crossed by therays of the bundle to be that defined by the two extreme points of thesurface S₂. This implies that the specifications of the bundle and ofthe surface are interdependent: if we wish to define the bundle as thatcomposed of the rays that impinge within the acceptance α before therefraction on S₁ and with the edges of the segment coincident with thetwo extreme points of the surface S₂, it will be necessary, in general,to carry out a ray-tracing on the surface S₁. In the case that thesurface S₁ is flat, this ray-tracing is unnecessary, since therefraction in this dioptric is trivial, and the specification of thebundle after the refraction is therefore immediate by application ofSnell's Law: it will be a type 1 bundle with acceptance angle equal toα′=sin⁻¹(1/n sin α), n being the refractive index of the lens L₁.

[0012] In order to simplify the explanation, and by way of an example,let us suppose that S₁ is a plane, that the input and output bundles areboth type 1, and that the two bundles are symmetrical with respect to anaxis, as FIG. 3 shows. For the other types of bundle the procedure isanalogous. The input bundle (specified after the refraction on S₁) isdefined by the acceptance angle (24) with value α′, and by the edges(25) and (26) of the surface S₂, which we shall call I and I′, and whichdetermine the segment we shall refer to as the entry aperture. Theoutput bundle is defined by the receiver, which is the segment of edges(27) and (51), called respectively R and R′, and by the angle ofillumination limited to the acceptance. angle (28) of value β (thenormal consideration when the sensitivity of the receiver is low forvery grazing angles, as is common in photodiodes or solar cells). Theedges O and O′ of the surface S₃ are the symmetrical points (29) and(30). This figure also shows the system of Cartesian coordinates (31)that will be used for the description, and whose origin is centered onthe receiver.

[0013] Input design parameters (apart from the profile of the surfaceS₁) are the angles α and β, the distance RR′, the refractive index ofthe dielectric materials to be used (n for the lens L₁ and n′ for L₂),the ordinate of point I, the abscissa of point O and the abscissa ofpoint P. The ordinate of point O is calculated immediately from itsabscissa, the distance RR′ and the angle β. However, the calculation ofthe abscissa of point I and of the ordinate of point P will be obtainedlater, as the result of the design.

[0014] The design procedure consists of three phases. In the first phasethe design conditions for the teeth of the surface S₂ (which will bedifferent for concentration and collimation) are chosen, supposing thatthey are of infinitesimal size. With these conditions the calculation ismade of the expressions that constitute the individual design of teethfor the different angles of incidence with respect to the mean normalvector of the tooth. Designed simultaneously in the second phase, withthe SMS method, are the surfaces S₂ and S₃ that couple the output andinput bundles, taking into account the expressions calculated in thefirst phase. Lastly, in the third phase, the teeth of the surface S₂ aregenerated with finite size (as manufactured in practice) on the basis ofthe infinitesimal teeth calculated in the previous phase.

[0015] There are different possible design modes, according to the levelof complexity of the finite-size teeth of the surface S₂ both in theirdesign in the third phase and in their manufacture. Thus, we can defineas basic mode that in which the profiles of the T faces are rectilinear,as standard mode that in which these profiles are arcs of circumferenceand as advanced mode that in which they are aspheric. The three modesconverge on one another when the size of the teeth is very small(providing an operating quality coincident with that predicted forinfinitesimal teeth), but their performance degrades differently whenthe size of the teeth is greater. In increasing order of quality are thebasic, standard and advanced modes. Since the design of the standard andadvanced modes is carried out from the basic mode, we shall begin bydescribing this before proceeding with the explanation of the others.

[0016] Let us consider for the first phase the description of a toothdesigned in the first quadrant operating as a concentrator as shown inFIG. 4.a. Given that the size of the tooth is infinitesimal (enlarged inthe figure), this means that, in the scale of the figure, adjacent teethare identical, and that the wavefronts associated with the edge rays areflat. The vector (32), which we shall call t, is the macroscopic tangentvector of the surface S₂. It is desired that the light incident throughsegment (33), of edges (34) and (35), with slope between that of rays(36) and (37), which we shall call, respectively, e(+) and e(″), istransmitted optimally through segment (38), of edges (39) and (40), withslope between that of rays (41) and (42), which we shall call,respectively, i (−) and i(+). To this end the following designcharacteristics will be imposed: (1) that no undesired incidences occur,and (2) that the irradiance on leaving the tooth is as uniform aspossible. Both characteristics are obtained on demanding the twofollowing conditions. On the one hand, that face V is parallel to thebisector of the impinging bundle, which coincides with the so-calledflow line of the bundle (Welford, Winston, 1989). Face V situated inthis way has the property of reflecting (through total internalreflection) the bundle without its geometry being modified. On the otherhand, it should be demanded that the ray e(−) that impinges at point(34) after the total internal reflection on face T and the refraction onface V, is transformed into the ray i(−) that passes through point (40).Note that rays i(−) transformed from rays e(+) and e(−) pass through allthe points of segment (38), but that rays i(+) emerge from only aportion of segment (38) (for this reason the irradiance is not uniformin (38), though it as uniform as possible, as required by condition(2)). Nevertheless, in the second phase the rays i(+) and i(−) will beused as though they emerged from the whole of segment (38), which meansthat it will not be possible to reach the thermodynamic limit ofconcentration/collimation (although the invention comes very close todoing so).

[0017] These two conditions for the design of the infinitesimal teeth,which guarantee their optimum functioning, constitute another innovationwith respect to the above-mentioned related patents, none of whichincludes these conditions.

[0018]FIG. 4.b shows a tooth for the basic design operating as acollimator. As it can be seen, the difference with respect to the caseof FIG. 4.a, in which it was designed as a concentrator, lies in thesecond imposed condition: in this case it is the ray e(+) that impingesat (34) that must be transformed into the ray i(+) that passes throughpoint (40).

[0019] On imposing the two mentioned conditions it is deduced that faceV is vertical, and the following expressions relating the anglesinvolved are obtained by trigonometrical calculations: $\begin{matrix}{{\tan \quad \delta} = {{\tan \quad \psi} + \frac{\sin \quad \psi}{\sqrt{n^{2} - {\sin^{2}\psi}}} + {\tan \quad \gamma}}} & \text{(Ec. 1.a)}\end{matrix}$

 n cos(2δ−α′)+sin φ=0  (Ec. 1.b)

n cos(2δ+α′)+sin φ′=0  (Ec. 1.c)

[0020] where φ, φ′, δ and γ are, respectively, the angles (54), (55),(56) and (57) shown in FIG. 4, n is the refractive index of the lens andψ≡φ in the design of the concentrator and ψ≡φ′ in that of thecollimator.

[0021] In the second phase, in which the profiles of the surfaces S₁ andS₂ are designed, the following steps are observed:

[0022] a) Select a value for the abscissa of point I (this value will berecalculated later).

[0023] b) Through the (inverse) application of Snell's Law, calculatethe vector tangent to S₃ at point O with the condition that the ray thatimpinges from I must be refracted at O toward R.

[0024] c) Calculate the angle δ of the infinitesimal tooth situated atpoint I with the condition that the ray i(+) associated with the toothis directed toward O. This can be achieved using the equation (Ec. 1.c),where the angle φ′ is calculated from the points I and O. Calculate alsothe angle φ using (Ec. 1.b), the angle γ using (Ec. 1.a), and from this,calculate t_(I)=(−cos γ, sin γ), which is the macroscopic vector tangentto S₂ at I.

[0025] d) Find the first section of S₃ above O with the condition thatthe rays proceeding from I are refracted on that portion toward thereceiver with angle of incidence β. The solution to this problem isgiven by the constancy of optical path from point I up to a flatwavefront sloped with the angle β, and is an ellipse. This constitutes aparticular case of the so-called Cartesian ovals. The tangent to S₃ atthese points can be found, once these have been calculated, by (inverse)application of Snell's Law as in step a). The last point of this portionis marked by the ray that, after refraction, passes through R′.

[0026] e) Find the following section of S₃ with the condition that therays proceeding from I are refracted on that portion toward point R′.Once again, the solution is given by the constancy of optical pathbetween the two points, and constitutes a particular case of Cartesianovals, and the tangent to S₃ at these points is found by (inverse)application of Snell's Law. The last point of this section, which willbe called H₀ and its tangent t_(H0), is that for whose calculation theray i(−) that comes from I has been used.

[0027] f) Rename I, t_(I), O and t_(O) as F₀, t_(F0), G₀ and t_(G0),respectively. From the sections of S₃ calculated in d) and f) select anumber M of uniformly-distributed points (for example, M=500) and namethem from F₁ to F_(M), with tangents t_(F1) to t_(FM). Note thatH₀≡F_(M) (y t_(H0)≡t_(FM)).

[0028] g) Find the following macroscopic point G₁ of the surface S₂ asthe point of intersection between the straight line that passes throughG₀ with direction vector t_(G0) and the trajectory of the ray refractedat F₁ proceeding from R (traced in the reverse direction). This ray isthe ray i(+) associated with the infinitesimal tooth at G₁, so that italso gives the angle φ′ at that point. With equations (Ec. 1.c), (Ec.1.b) and (Ec. 1.a) we can calculate, respectively, the angles δ, φ andγ, and from the last of these, t_(G1)=(−cos γ, sin γ), which is themacroscopic vector tangent to S₂ at G₁.

[0029] h) Calculate the following point H₁ of the surface S₃ as thepoint of intersection between the straight line that passes through H₀with direction vector t_(H0) and the ray i(−) associated with theinfinitesimal tooth of G₁. The tangent t_(H1) to S₃ at H₁ can once morebe found by (inverse) application of Snell's Law. Identify H₁≡F_(M+1)(and t_(H1)≡t_(FM+1)).

[0030] i) Repeat steps g) and h), increasing the subindices by one unit,until the abscissa of a point G_(n) is greater than the abscissa ofpoint P (selected as entry parameter). Since the precision on theabscissa of point P chosen is not important (and that, this precisionbeing determined by the value of the chosen parameter M in step f), itcan be improved through choice), it will be considered for what followsthat P≡G_(n).

[0031] The profile of the central region of S₂ (between P and P′) willbe calculated (together with the remaining portion of S₃), once againaccording to the edge-ray theorem, so that it directs the rays e(+)toward R′ and the rays e(−) toward R (Note that this assignation is theopposite of what was carried out in steps g) and h) for the exteriorportion of S₂). Given that the surfaces are continuous, this impliesthat the optical path from the wavefront associated with rays e(+) up toR′ will be constant, as will that from the wavefront associated withrays e(−) up to R. So that the surfaces S₂ and S₃ do not havediscontinuities in their respective vertices, the symmetry of the designobliges the two optical paths (measured with respect to symmetricalwavefronts), moreover, to be equal. This condition will allow toevaluate the initial choice of the abscissa of point I.

[0032] j) Find the tangent to S₂ at P so that the impinging ray e(−) istransformed after refraction into the ray i(+) calculated at point P instep i). Calculate the ray e(+) after the refraction at P. If the angleit forms with the horizontal is superior to the angle φ calculated atpoint P in step i), return to the beginning choosing a lower value forthe abscissa of point P.

[0033] k) Calculate a new section of S₃ next to point H_(n) found instep i) with the condition that the rays coming from P are refracted onthat portion toward point R′. Once more, the solution is given by theconstancy of optical path between the two points, and the tangent to S₃at these points is found by (inverse) application of Snell's Law. Thelast point of this section is that for whose calculation the ray e(+)after refraction at P has been used. Choose a number M′ ofuniformly-distributed points (for example, M′=50) and name them in a waycorrelative to the previous ones, that is, from H_(n+1) to H_(n+M′) (andfrom F_(M+n+1) to F_(M+n+M′)).

[0034] l) Calculate the optical paths C(+) and C(−) associated with therays e(+) up to R′ and the rays e(−) up to R, respectively.

[0035] m) Repeat the steps from a) to l) iterating on the value of theabscissa of point I until it is achieved that |1−C(+)/C(−)|<∈, with ∈being a pre-fixed margin of error (e.g., 0.0001).

[0036] n) Calculate the following point G_(n+1) of S₂ with the conditionthat the trajectory of the ray refracted at F_(n+1) coming from R(traced in the reverse direction) is transformed after refraction at thedesired point into a ray e(−). Once again, the solution is calculatedbecause the optical path C(−) is known, and the tangent to S₂ at G_(n+1)is found by (inverse) application of Snell's Law.

[0037] o) Calculate the following point H_(n+M′+1) of S₃ with thecondition that the trajectory of the ray e(+) refracted at G_(n+1) isdirected, after refraction at the desired point toward R′. Again, thesolution is calculated because the optical path C(+) is known, and thetangent to S₃ at H_(n+M′+1) is found by (inverse) application of Snell'sLaw.

[0038] p) Repeat steps n) and o) until the symmetry axis is reached,that is, until the abscissas of points G and H calculated are negative.

[0039] Finally, to conclude the basic design there remains only thethird phase, which involves the generation of the teeth of S₂ withfinite size (as they will be manufactured in practice) and faces withrectilinear profile on the basis of the macroscopic surface and theinfinitesimal teeth calculated in the previous phase. The proceduremoves from the edge toward the center of the lens observing thefollowing steps:

[0040] a) Select, for example, size D of the horizontal projection ofthe finite teeth. This size should be such that that the subsequentray-tracing shows no important degradation in the functioning of thedevice with respect to that obtained with size D/2.

[0041] b) Take as central points of the finite teeth those points G_(i)of the macroscopic surface between P and I whose abscissa differ lessfrom point I by an odd number of times D/2.

[0042] c) Define the slope of the face T of the finite tooth to whichG_(i) belongs as the slope of the face T defined at G_(i) by theinfinitesimal tooth. The face T of the finite tooth is extendedsymmetrically with respect to the point.

[0043] d) The faces V are thus situated at abscissas that differ frompoint I by a whole number of times D.

[0044] The basic concentrator design is complete. In this last phaseanother criterion can be taken for the generation of finite teeth, suchas that the distance between the upper and lower evolvent of the teethtakes the value D. The generation procedure is similar to thatdescribed, and the adjustment of the central points G_(i) of each toothcan carried out in an iterative way.

[0045] The standard mode differs from the basic mode in the third phase,where the faces T of the finite teeth have an arc of circumference as aprofile. The design procedure of this mode is similar to that of thebasic one. In the second phase, although the resulting design isidentical, the standard mode adds the calculation of the curvature ofthe faces T of the infinitesimal teeth (for its later use in the thirdphase), which constitutes a higher order of precision than that employedin the basic mode. In order to make this calculation the followingequation is used, which relates the radii of curvature of a surface andthose of the incident and refracted/reflected wavefronts:$\begin{matrix}{{\frac{n_{i}\cos^{2}\theta_{i}}{\rho_{i}} + \frac{n_{r}\cos^{2}\theta_{r}}{\rho_{r}}} = \frac{{n_{i}\cos \quad \theta_{i}} - {n_{r}\cos \quad \theta_{r}}}{\rho_{s}}} & \left( {{Ec}.\quad 2} \right)\end{matrix}$

[0046] where the subindices i, r and s refer to the incident wavefronts,refracted/reflected wavefronts and the surface, respectively, n denotesthe refractive index, θ the angle of the ray with respect to the normaland ρ the radius of curvature. Equation (Ec. 2) is applied to thereflection, making θ_(r)=θ_(i) and n_(r)=−n_(i).

[0047] In order to calculate the radius of curvature ρ_(sT) of the faceT of the infinitesimal teeth it is necessary to find previously theradius of curvature of S₃ at points F₁ to F_(M) during their calculationin steps d) and e) of the second phase. For this the expression (Ec. 2)is applied to the refraction at these points of the rays coming from I.In this case, for each point F_(k) and denoting by {overscore (AB)} thelength of the segment of edges A and B, we have ρ_(i)={overscore(IF_(k))}, ρ_(r)=∞ in step d) and ρ_(r)={overscore (R′F_(k))} in stepe).

[0048] It is in step f), in which the points G_(k) are calculated on thebasis of the points F_(k), where the desired values of ρ_(sT) should becalculated. The calculation involves the use of the expression (Ec. 2)for the three successive incidences undergone by the ray that goes (inthe reverse direction) from R toward F_(k). Given that in step f) thepoints and the normals to the surfaces are calculated, the angles ofincidence and of refraction/reflection, like the refractive indices, areknown parameters in the three incidences. In the first, at F_(k), as theradius of curvature ρ_(s) is already known and ρ_(i)={overscore(RF_(k))}, from (Ec. 2) we obtain the radius of curvature of therefracted wavefront ρ_(r1). For the second incidence, which occurs onthe face V of the tooth calculated at G_(k), the radius of curvature ofthe incident wavefront is ρ_(i)={overscore (G_(k)F_(k))}−ρ_(i) and theradius of curvature of the surface is known (ρ_(sV)=∞), so that from(Ec. 2) we obtain the radius of curvature of the refracted wavefrontρ_(r2). Finally, for the third incidence, which occurs on the face T ofthe tooth, it is known that ρ_(i)=−ρ_(r2) and ρ_(r3)=∞, so that (Ec. 2)can be solved with the radius of curvature ρ_(sT) as an unknown, whichwas the desired value.

[0049] Given that in step g) new points F_(j), are calculated, initiallycalled H_(k), and which will be used again in step f) on repeating it ash) indicates, it is also necessary to calculate the radius of curvatureof S₃ at these points. For this, the procedure is analogous to that ofthe calculation of ρ_(sT) previously indicated, using the trajectory ofthe ray used to calculate H_(k), which is the ray e(+) impinging atG_(k), and taking advantage of the fact that ρ_(sT) is already known.

[0050] The third phase of the standard mode, which concerns thegeneration of the teeth of finite size, differs from the basic mode inthat the T faces, instead of being rectilinear, are generated as arcs ofcircumference. The procedure of generating the teeth is analogous tothat seen for the basic mode, the only difference being that the face Tof the finite tooth to which the central point G_(i) of a finite toothbelongs is the arc of circumference that passes through that point, withthe slope and radius of curvature associated with the infinitesimaltooth, and that extends symmetrically with respect to the point. Thisconcludes the standard design mode.

[0051] Lastly, the advanced design mode is characterized by the faces Tof the teeth having an aspheric profile. The calculation of theseprofiles is made from the finished basic design (with finite teeth),observing the following steps:

[0052] a) Trace in the reverse direction the uniparametric ray bundlesthat leave from R and R′ and are refracted on S₃ and on the faces V ofthe finite teeth.

[0053] b) For each tooth, whose central point is G_(i), calculate theaspheric profile of the face T that passes through G_(i) and whosepoints Q are such that the ray that impinges vertically is reflected inaccordance with the direction bisecting of the rays of the uniparametricbundles that pass through Q calculated in a). This problem, which can beexpressed in the form of a first-order differential equation, has asingle solution when one ray—and only one of each bundle—passes througheach point Q.

[0054] The advanced design mode is finished. FIG. 11 shows an example ofan advanced design. As mentioned above, the aspheric profiles (54) ofthe facets allows to design them with bigger size than in the basic andstandard modes, and still maintain an excellent performance, even closeto the thermodynamic limit.

[0055] The description of the design procedures for the three modes(basic, standard and advanced) is finished.

[0056] The design is essentially similar in the case that the profilesof the faces V are not vertical lines, but have a pre-fixed slopingrectilinear, circular or aspheric profile. In fact, an aspect notconsidered in the descriptions of the designs concerns the fact that themanufacture of teeth with totally vertical faces V may be impractical(in the case of lens manufacture by plastic injection, removal of thepart from the mould is difficult). It is possible to correct thisaspect, for example, by considering design of the faces V withinclinations of a certain angle (in the range of 0.5° to 1° may besufficient), which entails appropriate modification of the equations(Ec. 1). Said inclination is also useful to avoid the undesired effectsproduced in practice by the rounding of the vertices of the teeth. As anegative consequence, a sloping face V means that it is not parallel toa flow line of the incident bundle, so that the reflection on that facewill modify (slightly) the geometry of the bundle. This means that thecharacteristic of angular transmission will be degraded (i.e., it willbe less stepped) with respect to that corresponding to vertical faces V.Meanwhile, the profiles of the faces V can be produced as arcs ofcircumference or pre-fixed aspheric curves to facilitate theirmanufacture even more (at the cost of making the production of the mouldmore difficult), by decreasing, for example, the curvature necessary forthe profiles of the faces T.

[0057] Another aspect not dealt with up to now concerns the fact thatthe condition imposed on the design of the infinitesimal teeth inconcentration that obliges the edge ray e(−) impinging at point (34) tobe transformed into the ray i(−) that passes through point (40) may berelaxed (i.e., allowing it to pass slightly above or below that point)without producing a serious degradation in functioning.

[0058] Taking into account all of these considerations, we can affirmthe usefulness of the possibility of the profiles of the faces V or Thaving at each point a slope modified by an angle of less than 2degrees.

[0059] The device described for concentrating radiation on a receivermay be axisymmetrical or cylindrical, and is characterized bytransforming the edge rays of an input extended ray bundle into edgerays of an output extended ray bundle that illuminates a receiver, bothbundles being defined in the plane of a cross-section (which containsthe symmetry axis in the axisymmetrical case, or is perpendicular to thedirection of symmetry in the cylindrical case), by means of: (a) a lensL₁ composed on one side of a refractive aspheric surface, S₁, on whichthe input bundle impinges, and on the other side, S₂, of anotherrefractive aspheric surface in its central region and with adiscontinuous-slope structure in its external region, whosecross-section is formed of teeth with two aspheric faces such that oneof them, V, is parallel to the flow lines of the bundle transmitted bythe dioptric S₁, and the other face, T, reflects the bundle by totalinternal reflection toward the face V where it is refracted so that noray intercepts the adjacent tooth and that the nearest edge ray to do sois tangent to that tooth; and (b) a second lens L₂ that surrounds thereceiver composed of an refractive aspheric surface on which the bundletransmitted by the lens L₁ impinges.

[0060] On the other hand, the device used for collimating the radiationgenerated by an emitter may be axisymmetrical or cylindrical, and ischaracterized by transforming the edge rays of an input extended raybundle generated by an emitter into edge rays of an output extended raybundle, both bundles being defined in the plane of a cross section, bymeans of: (a) a lens L₂ that surrounds the emitter composed of arefractive aspheric surface on which the input bundle impinges; and (b)a second lens L₁ composed on one side of a refractive aspheric surface,S₁, from which the output bundle leaves, and on the other side, S₂, ofanother refractive aspheric surface in its central region and with adiscontinuous-slope structure in its external region, whosecross-section is formed of teeth with two aspheric faces such that onone of them, V, the bundle transmitted by the dioptric S₃ is refractedso that all the rays are reflected by total internal reflection on theother face, T, that the edge ray nearest to not being reflected istangent to the profile of the tooth, and that the face V is parallel tothe flow lines of the bundle transmitted toward S₁.

[0061] The U.S. Pat. No. 5,577,493, November /1996 describes anaxisymmetric device which is qualitatively similar to this invention andit is used to collimate the radiation generated by an emitter and inwhich the bundles of rays are chosen to provide uniform irradiance inthree dimensions at the exit aperture. However, due to the restrictionsof their design method, their device will provide such performance onlywhen the angular spread of the ray bundles on passing through any of theoptical surfaces is small (<10°). Moreover, the design conditions of theinfinitesimal teeth used in this invention (Equations 1.a, 1.b, and1.c), which guarantee the optimal performance of the teeth, are not usedin the existing patent, which lead to the optical surfaces of theirinvention being substantially different, and their resulting opticalperformance being noticeably inferior.

[0062] The procedures described for the three design modes are equallyapplicable to the situation shown in FIG. 5, in which the lens L₂consists of two different dielectric materials separated by a spheric oraspheric refractive surface (43), with pre-fixed profile, justconsidering the refraction of the edge rays on this surface during theprocess.

[0063] A variant of the configuration described up to now consists insubstituting the refractive surface S₁ by a discontinuous-slope Fresnelstructure (44), as shown for example in FIG. 6 for the case of the flatand horizontal S₁. It is thus possible to use less dielectric material,which reduces its weight and absorption. The two surfaces, discontinuousand continuous, work in the same way. In fact, the profiles of theremaining optical surfaces are identical in the two designs. The onlydifference with respect to the trajectories of the rays is that thesecan now impinge on the vertical face of the steps, the face thatcoincides with the flow lines of the incident bundle. This implies, onceagain, that if these faces were mirrors the reflection of the rays onthem would not modify the geometry of the transmitted bundle. Althoughwhen the incidence takes place from the interior face of the dielectricmaterial this interface indeed behaves like a mirror due to thephenomenon of total internal reflection, this is not the case withincidence from the air, which leads to some losses. Nevertheless, forsmall acceptance angles α(<5°) these losses are negligible due to thecombination of two effects: the reflectivity of this interface, althoughnot 100%, is very high for large angles of incidence (and in the presentcase they will be superior to 90°−α), and the fraction of rays thatimpinge on the vertical faces from the air is also small if theacceptance angle is moderate.

[0064] The surface S₁ as a discontinuous-slope structure can also haveanother use, as FIG. 7 shows. In this case the flat dioptric of FIG. 2has been substituted by a discontinuous-slope structure with saw-toothedprofile (45) that diverts the input bundle to modify the direction ofthe flow lines (46). The lens is attached to a dielectric plate by meansof an adhesive with a refractive index slightly different from that ofthe lens. This structure refracts the rays of the incident bundle sothat they progress toward S₂ with a slight divergent direction. Thismeans that the face V of the teeth of the external region of S₂, ifdesigned with a non-null tilt angle to facilitate manufacture, willproduce a lesser degradation of the optical performance on being closerto (or even coinciding with) the divergent flow line. As the verticalface of the S₁ in turn causes a degradation (by blocking the raytrajectories), for each inclination of the faces V there is an optimumangle of divergence of the bundle, for which degradation is minimum.

[0065] Another possibility (which can also be combined with any of theprevious ones) consists in making the central portion of S₂ as adiscontinuous-slope Fresnel structure (47), as shown in FIG. 8.

[0066] Another possible configuration consists in designing the lenswith the surfaces S₁ and S₂ interchanged, so that the teeth appearinverted (48), as shown in FIG. 9. In the case of rotation symmetry, forits production by moulding, it is necessary for either the mould or thelens to be flexible, so that the lens can be extracted from the mould.In the case of translation symmetry this would be unnecessary, sincemanufacture could be by extrusion. The design procedure of the opticalsurfaces is common to all the configurations indicated.

[0067] In the proposed invention, used for concentrating radiation on areceiver, this could be optoelectronic, such as a photodiode,phototransistor or solar cell. On the other hand, if it is used forcollimating the radiation produced by an emitter, this could also beoptoelectronic, such as an LED, an IRED or a laser.

[0068] The manufacturing of the concentrator of this invention can becarried out using a diamond-tip lathe with numerical control (CNC) onplastic material, such as acrylic (PMMA). Another possibility worthy ofmention is that of the injection of the PMMA in a suitable mould, whichallows a production also covered by this patent, and which is shown inFIG. 10: the device can be manufactured with an optically inactiveportion (49) that joins the two lenses, and in such a way that theyconstitute a single piece that includes an interior space (53). Thejoining can be carried out by contact before solidification of the finalinjected part or by means of subsequent gluing. As it is a single piece,the space between the lenses is protected from dust and humidity. Thisspace can be evacuated or filled, if desired, with an inert gas. Theadhesion of the receiver or the emitter to the secondary can be carriedout by means of the casting of a transparent epoxy resin.

[0069] The improvements and differences this invention introduces withrespect to the mentioned state of the art can be summarized as follows:

[0070] (a) The designed surfaces and the faces of the teeth are suchthat the device couples in two dimensions the edge rays of two extendedray bundles, while those of the mentioned inventions couple only thecentral ray of the bundles or its first-order environment.

[0071] (b) In the case of the axisymmetric device to collimate theradiation generated by an emitter, the design ray bundles include as aparticular case the one that produces uniform irradiance the exitaperture, case considered in the U.S. Pat. No. 5,577,493, November/1996, but in said patent the design that is described there is onlyadecuate when the angular spread of the ray bundles on passing throughall of the optical surfaces is small (<10°).

[0072] (c) The conditions for the design of the infinitesimal teethfacets used in this invention (given by the Equations 1.a, 1.b y 1.c,which provide that the faces of the teeth are such that one guides thebundle as a flow line, they produce maximum uniformity of irradiance atthe exit of the tooth, and they avoid undesired incidence on theadjacent tooth) are not used in the previous state of the art, whichlead to the optical surfaces of the invention being substantiallydifferent, and also their resulting optical performance..

[0073] (d) Its use as a concentrator on a receiver.

[0074] (e) The cylindrical symmetry, where appropriate.

[0075] (f) Its possible manufacture as a single part with an interiorspace.

[0076] (g) The grouping of a set of devices fixed to a dielectric plate.

[0077] Differences (a) and (c) confer upon this invention an opticalperformance noticeably superior to that of the previous inventions,especially when the angular spread of the ray bundles as they passthrough any of the optical surfaces is large (>10°).

BRIEF DESCRIPTION OF FIGURES

[0078]FIG. 1: Commonly-used extended ray bundles. On the left, the type1 bundle, composed of the rays that impinge on a segment (1) of edges(6) and (7) forming an angle inferior to the acceptance angle of thebundle (2) with the perpendicular to that segment.

[0079] In the center, the type 2 bundle, composed of the rays thatintercept two given segments (3). The edge rays of this bundle are thosepassing through any of the edges (8, 9, 10 and 11) of the two givensegments.

[0080] On the right, a type 3 bundle composed of the rays that intercepta rectangle (4) and a semicircumference (5) of edges (12) and (13).

[0081]FIG. 2: Basic working principle of the invention as concentratorof radiation on a receiver (14). It comprises a lens (50) that surroundsthe receiver composed of a refractive aspheric surface (21), and asecond lens (15) whose upper side is a refractive aspheric surface (16)and whose lower side consists of another refractive aspheric surface(17) in its central region (between points 18 and 19) and adiscontinuous-slope structure (20) in its external region; whose faces(22) fundamentally refract the rays and the faces (23) reflect them bytotal internal reflection.

[0082]FIG. 3: System of Cartesian coordinates (31) and initial geometricparameters for carrying out the chosen design for concentratingradiation on a receiver. The input bundle is defined by the acceptanceangle (24) and by the entry aperture defined by the edges (25) and (26)of the surface S₂. The output bundle is defined by the segment of edges(27) and (51), which is the receiver and it is illuminated from surfaceS₃, whose edges are (29) and (30), with an angle of illumination limitedto the acceptance angle (28).

[0083]FIG. 4: Teeth of the surface S₂ designed in the first phase forthe device acting as (a) concentrator or (b) collimator. As they are ofinfinitesimal size (enlarged in the figure), the adjacent teeth areidentical, and the edge-ray bundles are parallel. It is desired that thelight incident through segment (33), of edges (34) and (35), with slopebetween that of rays (36) and (37), is transmitted optimally throughsegment (38), of edges (39) and (40), with slope between that of rays(41) and (42), which form angles (54) and (55) with the horizontal line,respectively. The geometry of the tooth with respect to its macroscopictangent vector (32) is defined by the angles (56) and (57).

[0084]FIG. 5: The lens L₂ can be produced with two different dielectricmaterials separated by a spheric or aspheric refractive surface (43).

[0085]FIG. 6: The surface S₁ can be substituted by a discontinuous-slopeFresnel structure (44), which reduces weight and absorption.

[0086]FIG. 7: The design of the S₁ as a discontinuous-slope structure(45) with saw-toothed profile allows transmission losses to be minimizedwhen the faces V do not coincide with flow lines (46) of the bundletransmitted by the continuous surface S₁.

[0087]FIG. 8: The central portion of the S₂ can be substituted by adiscontinuous-slope Fresnel structure (47).

[0088]FIG. 9: Configuration that consists in designing the lens with thesurfaces S₁ and S₂ interchanged, so that the teeth appear inverted (48).

[0089]FIG. 10: The device can be manufactured with an optically inactiveportion (49) that joins the two lenses, and in such a way that theyconstitute a single piece that includes an interior space (53).

[0090]FIG. 11: The device can be designed with aspheric faces (54) inthe advanced mode, which allows to design them with bigger size andstill maintain an excellent performance.

[0091] Industrial Application

[0092] The presented invention has direct applications in diversefields, such as that of radiation sensors, illumination systems withLEDs, wireless optical communications or photovoltaic solar energy.

[0093] In the field of sensors, the proposed invention allows theachievement of high sensitivities, close to the thermodynamic limit,without affecting the simplicity and compactness of the device. Also, inthe field of illumination with LED, this invention provides anoptimally-collimated bundle with a geometry readily compatible withcurrent production techniques.

[0094] In wireless optical communications, the control of angularresponse of the emitting and receiving devices and the use of almost allpossible directions of emission/reception in the design permitsconnections whose signal-noise relationship is close to the maximumpossible. Employed in reception, the proposed invention would use anoptoelectronic sensor as receiver (e.g., a photodiode orphototransistor); in transmission the invention would use anoptoelectronic emitter (LED, IRED or laser).

[0095] Finally, in photovoltaic applications this invention constitutesan appropriate device for high-concentration solar cells. Itsperformance close to the theoretical limit means that for a givenconcentration factor, the angular acceptance of the device is close tothe maximum possible, which is useful for permitting high tolerances inthe manufacture of the device itself and in the alignment of several ofthem to form a module (which can be made simply by gluing them to a flatpiece of glass), a light support structure for modules with lowsun-tracking accuracy.

1. Device for concentration of radiant energy characterized by beingaxisymmetrical or cylindrical and transforming the edge rays of an inputextended ray bundle into edge rays of an output extended ray bundle thatilluminates a receiver, both bundles being defined in the plane of across-section, by means of: a) A lens L₁ composed on one side of arefractive aspheric surface, S₁, on which the input bundle impinges, andon the other side, S₂, of another refractive aspheric surface in itscentral region and with a discontinuous-slope structure in its externalregion, whose cross-section is formed of teeth with two aspheric facessuch that one of them, V, is parallel to the flow lines of the bundletransmitted by the dioptric S₁, and the other face, T, reflects thebundle by total internal reflection toward the face V where it isrefracted so that no ray intercepts the adjacent tooth and that thenearest edge ray to do so is tangent to that tooth. b) A second lens L₂that surrounds the receiver composed of a refractive aspheric surface onwhich the bundle transmitted by the lens L₁ impinges.
 2. Device forconcentration of radiant energy according to claim 1 characterizedbecause it uses an optoelectronic receiver.
 3. Device for concentrationof radiant energy according to claims 1 and 2 characterized because theoptoelectronic receiver is a photodiode, a phototransistor or aphotovoltaic cell.
 4. Device for collimation of radiant energycharacterized by being axisymmetrical or cylindrical and transformingthe edge rays of an input extended ray bundle generated by an emitterinto edge rays of an output extended ray bundle, both bundles beingdefined in the plane of a cross-section, by means of: a) A lens L₂ thatsurrounds the emitter composed of a refractive aspheric surface on whichthe input bundle impinges. b) A second lens L₁ composed on one side of arefractive aspheric surface, S₁, from which the output bundle leaves,and on the other side, S₂, of another refractive aspheric surface in itscentral region and with a discontinuous-slope structure in its externalregion, whose cross-section is formed of teeth with two aspheric facessuch that on one of them, V, the bundle transmitted by the dioptric S₃is refracted so that all the rays are reflected by total internalreflection on the other face, T, that the edge ray nearest to not beingreflected is tangent to the profile of the tooth, and that the face V isparallel to the flow lines of the bundle transmitted toward S₁. 5.Device for collimation of radiant energy characterized by beingaxisymmetrical or cylindrical and transforming the edge rays of an inputextended ray bundle generated by an emitter into edge rays of an outputextended ray bundle, both bundles being defined in the plane of across-section, excluding the axisymmetric case in which the bundles ofrays are chosen to provide uniform irradiance in three dimensions at theexit aperture when the angular spread of the ray bundles on passingthrough all of the optical surfaces is smaller than 10°, by means of: a)A lens L₂ that surrounds the emitter composed of a refractive asphericsurface on which the input bundle impinges. b) A second lens L₁ composedon one side of a refractive aspheric surface, S₁, from which the outputbundle leaves, and on the other side, S₂, of another refractive asphericsurface in its central region and with a discontinuous-slope structurein its external region, whose cross-section is formed of teeth with twoaspheric faces such that on one of them, V, the bundle transmitted bythe dioptric S₃ is refracted so that all the rays are reflected by totalinternal reflection on the other face, T, that the edge ray nearest tonot being reflected is tangent to the profile of the tooth, and that theface V is parallel to the flow lines of the bundle transmitted towardS₁.
 6. Device for collimation of radiant energy characterized by beingaxisymmetrical or cylindrical and transforming the edge rays of an inputextended ray bundle generated by an emitter into edge rays of an outputextended ray bundle, both bundles being defined in the plane of across-section, excluding the axisymmetric case in which the bundles ofrays are chosen to provide uniform irradiance in three dimensions at theexit aperture, by means of: a) A lens L₂ that surrounds the emittercomposed of a refractive aspheric surface on which the input bundleimpinges. b) A second lens L₁ composed on one side of a refractiveaspheric surface, S₁, from which the output bundle leaves, and on theother side, S₂, of another refractive aspheric surface in its centralregion and with a discontinuous-slope structure in its external region,whose cross-section is formed of teeth with two aspheric faces such thaton one of them, V, the bundle transmitted by the dioptric S₃ isrefracted so that all the rays are reflected by total internalreflection on the other face, T, that the edge ray nearest to not beingreflected is tangent to the profile of the tooth, and that the face V isparallel to the flow lines of the bundle transmitted toward S₁. 7.Device for collimation of radiant energy according to claims 4 to 6characterized because it uses an optoelectronic emitter.
 8. Device forcollimation of radiant energy according to claims 4 to 7 characterizedbecause the optoelectronic emitter is an LED, an IRED or a laser. 9.Device for concentration or collimation of radiant energy according toclaims 1 to 8 characterized because the profiles of the faces of theteeth have at each point a slope modified by an angle of less than 2degrees.
 10. Device for concentration or collimation of radiant energyaccording to claims 1 to 9 characterized because the profile of the S₁is circular or flat.
 11. Device for concentration or collimation ofradiant energy according to claims 1 to 10 characterized because thesurfaces S₁ and S₂ of the lens are interchanged, so that the teethappear inverted.
 12. Device for concentration or collimation of radiantenergy according to claims 1 to 11 characterized because S₁ has asaw-toothed profile that diverts the input bundle to modify thedirection of the flow lines.
 13. Device for concentration or collimationof radiant energy according to claims 1 to 12 characterized because S₁or the refractive surface of the central portion of S₂, or both, arediscontinuous-slope Fresnel structures.
 14. Device for concentration orcollimation of radiant energy according to claims 1 to 13 characterizedbecause the lens L₂ comprises two different dielectric materialsseparated by a spheric or aspheric refractive surface.
 15. Device forconcentration or collimation of radiant energy according to claims 1 to14 characterized because the cross-section of the teeth of S₂ have faceswith circular or rectilinear profiles.
 16. Device for concentration orcollimation of radiant energy according to claims 1 to 15 characterizedby being manufactured with an optically inactive portion that joins thetwo lenses so that they constitute a single part that includes aninterior space.
 17. Device for concentration or collimation of radiantenergy characterized by being composed of a set of devices according toclaim 1 to 16 fixed to a dielectric plate.